To achieve high-speed nitride-based high electron mobility transistors (HEMTs), both lateral and vertical scaling are required for future device fabrication. The large polarization difference between AlN and GaN provides extremely high electron densities at the heterointerface covered by only ~3-4 nm AlN barrier, which makes AlN/GaN heterojunction the ultimate nitride structure for high-frequency applications. This work includes the study of MBE growth of single AlN/GaN heterojunctions, theoretical study of 2DEG scattering mechanisms, and device issues of removing buffer leakage with polarization engineering and decreasing contact resistance with band diagram engineering. High-quality single AlN/GaN heterojunctions with RFMBE are reported, which leads to high-conductivity two-dimensional electron gases. The sheet densities can be tuned between 5e12-5e13 /cm^2 by varying the AlN thickness from 2-7 nm. By optimizing the MBE growth conditions, record low sheet resistances in the range of ~128 ohm/sq has been achieved. As a theoretical work, remote surface roughness (RSR) scattering is studied as a new scattering mechanism in AlN HEMTs. In both depletion-mode and enhancement-mode HEMTs with ultra-scaled AlN barriers, RSR scattering rate is in the same order of polar optical phonon scattering rate, which is the dominant scattering in HEMTs at room temperature. This indicates that to achieve high-performance HEMTs, both high-quality growth and processing techniques are required. Large buffer leakage and ohmic contact resistance are two factors that heavily degrade high-speed device performance. With polarization engineering, the first dopant-free epitaxial solution for the buffer leakage has been developed on semi-insulating GaN substrate. With 1.5 nm AlN nucleation layer grown in the N-rich regime, the buffer leakage is greatly reduced and reaches 1 mA/mm at DC bias of 200 V. This improvement increases the On/Off ratio by more than 4 orders of magnitude from 100 to 1e6. Band diagram engineering is applied in ohmic contact study. Due to the high barrier thickness, it is very hard to achieve ohmic contact less than 1 Ohm-mm with traditional annealing technique. Regrown silicon doped GaN and graded InGaN/InN contacts have been demonstrated. Contact resistance as low as ~0.4 Ohm-mm has been achieved with n-GaN regrowth. MBE growth for graded InGaN/InN has been developed. X-ray diffraction measurements have been performed for material characterization.